Other Physics · JEE Main previous year questions

A paratrooper jumps from an aeroplane and opens a parachute after $2\text{ s}$ of free fall and starts decelerating with $3{\text{ m/s}}^2$. At $10\text{ m}$ height from ground, while descending with the help of parachute, the speed of paratrooper is $5\text{ m/s}$. The initial height of the airplane is _____ m. ($g=10{\text{ m/s}}^2$)

1. A.92.5
2. B.62.5
3. C.20
4. D.82.5

A body of mass $14\mathrm{kg}$ initially at rest explodes and breaks into three fragments of masses in the ratio $2:2:3$. The two pieces of equal masses fly off perpendicular to each other with a speed of $18m/s$ each. The velocity of the heavier fragment is ____ $m/s$.

1. A.$24\sqrt{2}$
2. B.12
3. C.$12\sqrt{2}$
4. D.$10\sqrt{2}$

A $4\mathrm{kg}$ mass moves under the influence of a force $\vec{F}=\left(4t^3\hat{i}-3t\hat{j}\right)\mathrm{N}$ where $t$ is the time in second. If mass starts from origin at $t=0$, the velocity and position after $t=2\mathrm{s}$ will be:

1. A.$\vec{v}=3\hat{i}+\frac{3}{2}\hat{j}\vec{r}=\frac{6}{5}\hat{i}+\hat{j}$
2. B.$\vec{v}=4\hat{i}-\frac{3}{2}\hat{j}\vec{r}=\frac{6}{5}\hat{i}-\hat{j}$
3. C.$\vec{v}=4\hat{i}-\frac{3}{2}\hat{j}\vec{r}=\frac{8}{5}\hat{i}-\hat{j}$
4. D.$\vec{v}=4\hat{i}+\frac{5}{2}\hat{j}\vec{r}=\frac{8}{5}\hat{i}+2\hat{j}$

1. A.$100\sqrt{3}$
2. B.$\frac{200}{\sqrt{3}}$
3. C.$200\sqrt{6}$
4. D.$200\sqrt{3}$

The r.m.s. speed of oxygen molecules at 47 °C is equal to that of the hydrogen molecules kept at _________ °C. (Mass of oxygen molecule/mass of hydrogen molecule = 32/2)

1. A.-100
2. B.-253
3. C.-20
4. D.-235

There are ' $n$ ' number of identical electric bulbs, each is designed to draw a power $p$ independently from the mains supply. They are now joined in series across the mains supply. The total power drawn by the combination is :

1. A.$np$
2. B.$p$
3. C.$\frac{p}{n^2}$
4. D.$\frac{p}{n}$

Consider a completely full cylindrical water tank of height $1.6\mathrm{m}$ and of cross-sectional area $0.5{\mathrm{m}}^2$. It has a small hole in its side at a height $90\mathrm{cm}$ from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load $50\mathrm{kg}$ is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is: $(g=10m/{\mathrm{s}}^2)$

1. A.$2m/s$
2. B.$5m/s$
3. C.$3m/s$
4. D.$4m/s$

1. A.$2.5m/{\mathrm{s}}^2$
2. B.$3.5m/{\mathrm{s}}^2$
3. C.$0.25m/{\mathrm{s}}^2$
4. D.$0.35m/{\mathrm{s}}^2$

Pressure of an ideal gas, contained in a closed vessel, is increased by $0.4\%$ when heated by $1^{\circ }\mathrm{C}$. Its initial temperature must be:

1. A.$2500\mathrm{K}$
2. B.$25^{\circ }\mathrm{C}$
3. C.$250^{\circ }\mathrm{C}$
4. D.$250\mathrm{K}$

1. A.10 N
2. B.0 (zero)
3. C.$10\sqrt{2}\text{ N}$
4. D.20 N

1. A.$1\mathrm{V}$
2. B.$\frac{1}{4}\mathrm{V}$
3. C.$\frac{3}{4}\mathrm{V}$
4. D.$\frac{2}{5}\mathrm{V}$

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

1. A.low thermal conductivity and high electrical conductivity
2. B.low thermal conductivity and low electrical conductivity
3. C.high thermal conductivity and high electrical conductivity
4. D.high thermal conductivity and low electrical conductivity

A cup of coffee cools from $90^{\circ }\mathrm{C}$ to $80^{\circ }\mathrm{C}$ in $t$ minutes when the room temperature is $20^{\circ }\mathrm{C}$. The time taken by the similar cup of coffee to cool from $80^{\circ }\mathrm{C}$ to $60^{\circ }\mathrm{C}$ at the same room temperature is:

1. A.$\frac{13}{5}t$
2. B.$\frac{10}{13}t$
3. C.$\frac{5}{13}t$
4. D.$\frac{13}{10}t$

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ________.

The temperature of a body in air falls from $40^{\circ }\mathrm{C}$ to $24^{\circ }\mathrm{C}$ in 4 minutes. The temperature of the air is $16^{\circ }\mathrm{C}$. The temperature of the body in the next 4 minutes will be :

1. A.${\frac{28}{3}}^{\circ }\mathrm{C}$
2. B.${\frac{56}{3}}^{\circ }\mathrm{C}$
3. C.${\frac{42}{3}}^{\circ }\mathrm{C}$
4. D.${\frac{14}{3}}^{\circ }\mathrm{C}$

1. A.zero
2. B.$40\pi$
3. C.$5\pi$
4. D.$10\pi$

1. A.
2. B.
3. C.
4. D.

The position vector of a moving body at any instant of time is given as $\vec{r}=\left(5t^2\hat{i}-5t\hat{j}\right)\text{m}$. The magnitude and direction of velocity at $t=2s$ is,

1. A.$5\sqrt{17}\text{ m/s}$, making an angle of ${\tan }^{-1}4$ with - ve Y axis
2. B.$5\sqrt{15}\text{ m/s}$, making an angle of ${\tan }^{-1}4$ with + ve X axis
3. C.$5\sqrt{17}\text{ m/s}$, making an angle of ${\tan }^{-1}4$ with + ve X axis
4. D.$5\sqrt{15}\text{ m/s}$, making an angle of ${\tan }^{-1}4$ with $-\text{ve }Y$ axis

Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g.

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

1. A.64 E
2. B.16 E
3. C.E
4. D.256 E

A heavy iron bar, of weight $W$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person is :

1. A.$W\sin \theta$
2. B.$W$
3. C.$\frac{W}{2}$
4. D.$W\cos \theta$

The energy equivalent of $1\text{ g}$ of substance is :

1. A.$5.6\times 10^{26}\text{ MeV}$
2. B.$5.6\times 10^{12}\text{ MeV}$
3. C.$5.6\text{ eV}$
4. D.$11.2\times 10^{24}\text{ MeV}$

An astronaut takes a ball of mass $m$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $318.5\text{ km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x\frac{\mathrm{G}{\mathrm{M}}_{\mathrm{e}}\mathrm{m}}{21{\mathrm{R}}_e}$. The value of $x$ is (take ${\mathrm{R}}_e=6370\text{ km}$) :

1. A.12
2. B.11
3. C.9
4. D.10

If $\vec{a}$ and $\vec{b}$ make an angle ${\cos }^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$. The integer value of $n$ is ______.

A star has 100% helium composition. It starts to convert three ${}^4\mathrm{He}$ into one ${}^{12}\mathrm{C}$ via triple alpha process as ${}^4\mathrm{He}+{}^4\mathrm{He}+{}^4\mathrm{He}\to {}^{12}\mathrm{C}+\mathrm{Q}$. The mass of the star is $2.0\times 10^{32}\text{ kg}$ and it generates energy at the rate of $5.808\times 10^{30}\text{ W}$. The rate of converting these ${}^4\mathrm{He}$ to ${}^{12}\mathrm{C}$ is $\mathrm{n}\times 10^{42}{\text{ s}}^{-1}$, where $\mathrm{n}$ is ______. [ Take, mass of ${}^4\mathrm{He}=4.0026\text{u}$, mass of ${}^{12}\mathrm{C}=12\text{u}$]